Multiple Houston family sources tell TMZ ... it's absurd that Nick has a lawyer putting them on blast for denying him the right to see his girlfriend. The sources say Nick has never once tried to make his way inside the hospital.

As for the picture of Nick in front of the hospital ... they think it was just for the cameras -- he never tried entering the building.

Nick's lawyer Randy Kessler insists his client has made the effort but has been blocked, but the lawyer says he's not taking legal action so Nick can gain entrance.

On Nick's side there's also this ... we reported several of Bobby Brown's relatives threatened to put "hands on him" if Nick ever showed up.

TMZ broke the story ... there's a criminal investigation surrounding the circumstances of Bobbi Kristina's near drowning, and Nick is the target.